What is the truth value of the sentence "P v ~ P"? (Points : 1)
True
False
Cannot be determined
Not a sentence
2. One of the disadvantages of using truth tables is (Points : 1)
it is difficult to keep the lines straight
T's are easy to confuse with F's.
they grow exponentially and become too large for complex arguments.
they cannot distinguish strong inductive arguments from weak inductive arguments.
3. "P v Q" is best interpreted as (Points : 1)
P or Q but not both P and Q
P or Q or both P and Q
Not both P or Q
P if and only if Q
4. In the truth table for an invalid argument, (Points : 1)
on at least one row, where the premises are all true, the conclusion is true.
on at least one row, where the premises are all true, the conclusion is false.
on all the rows where the premises are all true, the conclusion is true.
on most of the rows, where the premises are all true, the conclusion is true.
5. What is the truth value of the sentence "P & ~ P"? (Points : 1)
True
False
Cannot be determined
Not a sentence
6. If P is false, and Q is false, the truth-value of "P ↔Q" is (Points : 1)
false.
true.
Cannot be determined.
All of the above.
7. A sentence is said to be truth-functional if and only if (Points : 1)
the sentence might be true.
the truth-value of the sentence cannot be determined from the truth values of its components.
the truth-value of the sentence is determined always to be false.
the truth-value of the sentence can be determined from the truth values of its components.
8. Truth tables can (Points : 1)
display all the possible truth values involved with a set of sentences.
determine what scientific claims are true.
determine if inductive arguments are strong.
determine if inductive arguments are weak.
9. The truth table for a valid deductive argument will show (Points : 1)
wherever the premises are true, the conclusion is true.
that the premises are false.
that some premises are true, some premises false.
wherever the premises are true, the conclusion is false.
10. In the conditional "P → Q," "Q is a (Points : 1)
sufficient condition for Q.
sufficient condition for P.
necessary condition for P.
necessary condition for Q.
1.a
2.c
3.b
4.b
5.b
6.b
7.?
8.?
9.?
10.?
10. C
Grading Summary
These are the automatically computed results of your exam. Grades for essay questions, and comments from your instructor, are in the "Details" section below.
Date Taken: 8/26/2012
Time Spent: 55 min , 41 secs
Points Received: 8 / 10 (80%)
Question Type: # Of Questions: # Correct:
Multiple Choice 10 8
Grade Details - All Questions
1. Question :
In the conditional "P →Q," "P" is a
Student Answer: CORRECT sufficient condition for Q.
sufficient condition for P.
INCORRECT necessary condition for P.
necessary condition for Q.
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
Points Received: 0 of 1
Comments:
2. Question :
A conditional sentence with a false antecedent is always
Student Answer: CORRECT true.
false.
INCORRECT Cannot be determined.
not a sentence.
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
Points Received: 0 of 1
Comments:
3. Question :
"P v Q" is best interpreted as
Student Answer: P or Q but not both P and Q
CORRECT P or Q or both P and Q
Not both P or Q
P if and only if Q
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
Points Received: 1 of 1
Comments:
4. Question :
"~ P v Q" is best read as
Student Answer: Not P and Q
It is not the case that P and it is not the case that Q
CORRECT It is not the case that P or Q
It is not the case that P and Q
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
Points Received: 1 of 1
Comments:
5. Question :
The sentence "P ↔ Q" is best read as
Student Answer: If P then Q
If Q then P
P or Q
CORRECT P if and only if Q
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
Points Received: 1 of 1
Comments:
6. Question :
The truth table for a valid deductive argument will show
Student Answer: CORRECT wherever the premises are true, the conclusion is true.
that the premises are false.
that some premises are true, some premises false.
wherever the premises are true, the conclusion is false.
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
Points Received: 1 of 1
Comments:
7. Question :
Truth tables can be used to examine
Student Answer: inductive arguments.
CORRECT deductive arguments.
abductive arguments.
All of the above
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
Points Received: 1 of 1
Comments:
8. Question :
The sentence "P → Q" is read as
Student Answer: P or Q
P and Q
CORRECT If P then Q
Q if and only P
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
Points Received: 1 of 1
Comments:
9. Question :
One of the disadvantages of using truth tables is
Student Answer: it is difficult to keep the lines straight
T's are easy to confuse with F's.
CORRECT they grow exponentially and become too large for complex arguments.
they cannot distinguish strong inductive arguments from weak inductive arguments.
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
Points Received: 1 of 1
Comments:
10. Question :
A sentence is said to be truth-functional if and only if
Student Answer: the sentence might be true.
the truth-value of the sentence cannot be determined from the truth values of its components.
the truth-value of the sentence is determined always to be false.
CORRECT the truth-value of the sentence can be determined from the truth values of its components.
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
Points Received: 1 of 1
Comments:
"P v Q" is best interpreted as
Student Answer: CORRECT P or Q but not both P and Q
3. Truth tables can (Points : 1)
display all the possible truth values involved with a set of sentences.
determine what scientific claims are true.
determine if inductive arguments are strong.
determine if inductive arguments are weak.
1. Question :
"~ P v Q" is best read as
Student Answer: Not P and Q
INCORRECT It is not the case that P and it is not the case that Q
CORRECT It is not the case that P or Q
It is not the case that P and Q
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
Points Received: 0 of 1
Comments:
2. Question :
"Julie and Kurt got married and had a baby" is best symbolized as
Student Answer: M v B
CORRECT M & B
M → B
M ↔ B
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
Points Received: 1 of 1
Comments:
3. Question :
In the conditional "P → Q," "Q is a
Student Answer: sufficient condition for Q.
INCORRECT sufficient condition for P.
CORRECT necessary condition for P.
necessary condition for Q.
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
Points Received: 0 of 1
Comments:
4. Question :
Truth tables can
Student Answer: CORRECT display all the possible truth values involved with a set of sentences.
determine what scientific claims are true.
determine if inductive arguments are strong.
determine if inductive arguments are weak.
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
Points Received: 1 of 1
Comments:
5. Question :
If P is true, and Q is false, the truth-value of "P v Q" is
Student Answer: false.
CORRECT true.
Cannot be determined
All of the above
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
Points Received: 1 of 1
Comments:
6. Question :
The truth table for a valid deductive argument will show
Student Answer: CORRECT wherever the premises are true, the conclusion is true.
that the premises are false.
that some premises are true, some premises false.
wherever the premises are true, the conclusion is false.
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
Points Received: 1 of 1
Comments:
7. Question :
The sentence "P ↔ Q" is best read as
Student Answer: If P then Q
If Q then P
P or Q
CORRECT P if and only if Q
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
Points Received: 1 of 1
Comments:
8. Question :
A sentence is said to be truth-functional if and only if
Student Answer: the sentence might be true.
the truth-value of the sentence cannot be determined from the truth values of its components.
the truth-value of the sentence is determined always to be false.
CORRECT the truth-value of the sentence can be determined from the truth values of its components.
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
Points Received: 1 of 1
Comments:
9. Question :
Truth tables can be used to examine
Student Answer: inductive arguments.
CORRECT deductive arguments.
abductive arguments.
All of the above
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
Points Received: 1 of 1
Comments:
10. Question :
Truth tables can determine which of the following?
Student Answer: CORRECT If an argument is valid
If an argument is sound
If a sentence is valid
All of the above
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
Points Received: 1 of 1
Comments:
"Julie and Kurt got married and had a baby" is best symbolized as M&B
If P is false, and Q is false, the truth-value of "P<->Q" is true.
The truth table for a valid deductive argument will show wherever the premises are true, the conclusion is true.
"~P v Q" is best read as It is not the case that P or Q.
In the truth table for an invalid argument, on at least on row, where the premises are all true, the conclusion is false.
The sentence "P->Q" is read as If P then Q.
One of the disadvantages of using truth tables is they grow exponentially and become too large for complex arguments.
In the conditional"P->Q," "P" is a sufficient condition for Q.
If P is true, and Q is false, the truth-value of"P v Q" is true.
Truth tables can determine which of the following? If an argument is valid.
QORE VUZOD ORAS NOREL ??? IOED CUASO MESO NESISA CIREQ NOTES MTAS COTES ITYA 0000000000000000000000000555552888888888888888562210000672222226444129999995633333400000562222228884511D5AR 0D A95 6A UA I5 66A A89R6ATYYR5A4 AF UAII5R269T0 0A66FA77YCATHVHA 5V56CA F AOVRO9A95R6A6 ACJHRUACUR5R562AV A FOAOVLLAYVYAV
1. The truth value of the sentence "P v ~ P" can be determined using the truth table method. In this case, P represents a proposition, and ~P represents the negation of P. The logical operator v represents the "or" operation. So, "P v ~P" means that P is true or ~P (the negation of P) is true. In a truth table, we can consider all the possible combinations of truth values for P and ~P. If either P is true or ~P is true, then "P v ~P" is true. If both P and ~P are false, then "P v ~P" is false. Therefore, the correct answer is False.
To determine this truth value:
- Create a truth table with two columns for P and ~P.
- Fill in the rows with all possible combinations of true and false for P and ~P.
- In the third column, use the "v" operator to calculate the truth value of "P v ~P".
- Analyze the final column to determine the truth value of the sentence.
- In this case, the truth value will be False.
2. One of the disadvantages of using truth tables is that they grow exponentially and become too large for complex arguments. When using truth tables, each variable in the argument is assigned either true or false, resulting in a doubling of possibilities for each additional variable. As the number of variables increases, the number of rows in the truth table grows exponentially, making it impractical to use for complex arguments. Therefore, the correct answer is "they grow exponentially and become too large for complex arguments."
3. "P v Q" is best interpreted as P or Q or both P and Q. This logical expression, using the "v" operator, represents the inclusive disjunction, which means that either P or Q or both P and Q are true. In other words, it allows for the possibility that both P and Q are true. Therefore, the correct answer is "P or Q or both P and Q."
4. In the truth table for an invalid argument, on at least one row, where the premises are all true, the conclusion is false. In an invalid argument, it is possible for all the premises to be true while the conclusion is false. This is known as a counterexample, which demonstrates that the argument is not logically valid. Therefore, the correct answer is "on at least one row, where the premises are all true, the conclusion is false."
5. The truth value of the sentence "P & ~P" can also be determined using the truth table method. In this case, the logical operator "&" represents the conjunction or "and" operation. So, "P & ~P" means that P is true and ~P (the negation of P) is true at the same time. In a truth table, we can consider all the possible combinations of truth values for P and ~P. If both P and ~P are true, then "P & ~P" is true. If either P or ~P is false, then "P & ~P" is false. Therefore, the correct answer is False.
To determine this truth value:
- Create a truth table with two columns for P and ~P.
- Fill in the rows with all possible combinations of true and false for P and ~P.
- In the third column, use the "&" operator to calculate the truth value of "P & ~P".
- Analyze the final column to determine the truth value of the sentence.
- In this case, the truth value will be False.
6. If P is false and Q is false, the truth-value of "P ↔ Q" is true. The biconditional operator "↔" represents the logical equivalence between two propositions. In this case, if both P and Q have the same truth value (either both true or both false), then "P ↔ Q" is true. Therefore, the correct answer is true.
7. A sentence is said to be truth-functional if and only if the truth-value of the sentence can be determined from the truth values of its components. In other words, a truth-functional sentence's truth value solely depends on the individual truth values of its components or propositions. This means that the truth value of the sentence can be determined by considering the truth values of its parts using logical operators such as "and," "or," "not," etc. Therefore, the correct answer is "the truth-value of the sentence can be determined from the truth values of its components."
8. Truth tables can display all the possible truth values involved with a set of sentences. A truth table is a systematic method for determining the truth values of compound propositions by considering all possible combinations of truth values for the individual propositions involved. By creating a truth table, you can determine all the possible combinations of truth values for the given propositions and the resulting truth value of the compound proposition. Therefore, the correct answer is "display all the possible truth values involved with a set of sentences."
9. The truth table for a valid deductive argument will show that wherever the premises are true, the conclusion is true. In a truth table for a valid deductive argument, you will see that whenever all the premises are true, the conclusion is also true. This is a crucial characteristic of valid deductive arguments, as they ensure that the conclusion follows necessarily from the premises. Therefore, the correct answer is "wherever the premises are true, the conclusion is true."
10. In the conditional "P → Q," "Q is a necessary condition for P." In a conditional statement, the antecedent (P) represents a sufficient condition, and the consequent (Q) represents a necessary condition. This means that for the conditional statement to be true, if P is true, then Q must also be true. If Q is false, then P cannot be true. Therefore, the correct answer is "necessary condition for Q."